First, gas-particle flows are classified based on particle-particle interaction. Next, methods of numerical analysis of gas-particle flows are classified based on the concept of length scale. That is, the methods are classified into micro-, meso- and macro-scale approaches. The scale-based classification is applied to gas-phase and particulate phase, respectively. Most of existing models of multiphase flows are categorized into one of the combination of scale-based models for gas and particles. After the classification, description focuses on the discrete particle simulation which belongs to the micro-scale approach for the particle phase. The advantage of the particle-micro approach is to deal with particle-particle interaction in the rational way. To treat the particle-to-particle interaction mathematically, techniques named DEM (Distinct Element Method) and DSMC (Direct Simulation Monte Carlo) have been developed. DEM is a powerful means for the contact-dominated flows and DSMC method for the collision-dominated flows. Combining DEM or DSMC with CFD (computer fluid dynamics), applications of the discrete particle simulation have drastically expanded into many industrial flows because both particle-to-particle and particle-to-fluid interactions have significant effects on most industrial flows. Various examples of simulations are shown; such as dense phase pneumatic conveying, spouted bed, fast circulating fluidized bed and so on. (c) 2007 Elsevier Ltd. All rights reserved.